论文标题
调查和控制非自主动力学系统的发散条件
Divergence Conditions for Investigation and Control of Nonautonomous Dynamical Systems
论文作者
论文摘要
本文描述了一种研究非自主动力学系统稳定性的新方法。该方法基于矢量场的流量和差异，并与Lyapunov函数方法耦合。制定了必要和足够的稳定条件。结果表明，必要的稳定性条件与位于动力学系统平衡点的源（向内向内）的连续性方程的积分和差异形式有关。足够的稳定性条件用于设计状态反馈控制定律。拟议的控制定律被发现是部分差分不平等的解决方案，而基于Lyapunov技术的控制定律是从代数不平等的解决方案中找到的。这些示例说明了所提出方法与某些现有方法相比的有效性。
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and sufficient stability conditions are formulated. It is shown that the necessary stability conditions are related to the integral and differential forms of continuity equations with the sources (the flux is directed inward) located in the equilibrium points of the dynamical system. The sufficient stability conditions are applied to design the state feedback control laws. The proposed control law is found as a solution of partial differential inequality, whereas the control law based on Lyapunov technique is found from the solution of algebraic inequality. The examples illustrate the effectiveness of the proposed method compared with some existing ones.
